PHY1033C/HIS3931/IDH 3931 : Discovering Physics: The Universe and Humanity s Place in It Fall Prof. Peter Hirschfeld, Physics

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1 PHY1033C/HIS3931/IDH 3931 : Discovering Physics: The Universe and Humanity s Place in It Fall 2016 Prof. Peter Hirschfeld, Physics

2 Announcements HW 6 due today Reading: Gregory, Chapter 9, pp ; Chapter 7, pp HW 5 comment

3 Answer: Kepler: R 3 T 2 R 3 = a T 2 a = slope of R 3 - T 2 graph

4 For Saturn rise/run = 1.15x10 8 /2.89x10 27 =4.0x10-20 so T 2 [days 2 ]= (4.0x10-20 ) R 3 [km 3 ] Saturn Jupiter All the others Equally spaced points!!!

5 Clicker question 1 Newton s law of universal gravitation 1. Says that the grav. force between planets is proportional to 1/r 3 2. Says that the force between objects is proportional to the masses of the two objects 3. Applies only to objects inside the orb of the moon 4. Applies only to apples and the moon, but not planets 5. Requires two objects to be in direct mechanical contact

6 Last time: Newton s law of universal gravitation Mutual force of attraction between any two objects with mass in the universe m 1 m 2 F g F = G g r m 1 r m 2 2

7 Last time: Newton s Laws of motion 1. An object moves with a velocity that is constant in magnitude and direction, unless acted on by a nonzero total force (inertia=tendency to stay in same state of motion, measured by mass) 2. F=ma Applied total force F is proportional to the acceleration a, with prop. const. (mass) m. 3. For every action there is an equal and opposite reaction

8 Discussion question A lazy horse argues, I can t pull the wagon since I can never exert more of a force on it than it exerts on me, according to Newton s 3 rd law. What is the key reason the cart can really move? C=cart H=horse G=ground

9 Newton at

10 Peek at timeline

11 To Cambridge University as subsizar in 1661 Dominated by Aristotle Newton read Descartes, Galileo, Kepler and others on his own Plague forced university to close Newton goes home to Woolsthorp Annus mirabilis of 1666 Calculus Problem of the Moon

12 The Problem:????? Why does the moon orbit the earth?

13 Complicating the Problem Galileo s explanation: circular inertial motion For Galileo natural motion is uniform and circular

14 So for Newton straight line motion is natural and curved motion is constrained (First Law) That means to interrupt natural motion requires the presence of an unbalanced force (Second Law)

16 The legend of the apple "After dinner, the weather being warm, we went into the garden and drank tea, under the shade of some apple trees, only he and myself. Amidst other discourse, he told me he was in the same situation as when formerly the notion of gravitation came into his mind. It was occasioned by the fall of an apple as he sat in a contemplative mood." William Stuckley, 1726

17 As he sat alone in a garden, he fell into a speculation on the power of gravity: that as this power is not found sensibly diminished at the remotest distance from the center of the earth to which we can rise, neither at the tops of the loftiest buildings, nor even on the summits of the highest mountains, it appeared to him reasonable to conclude that this power must extend much farther than was usually thought. Why not as high as the moon, said he to himself? And if so, her motion must be influenced by it; perhaps she is retained in her orbit thereby....

18 What he already knew 1. a = 32 ft/sec 2 (by measuring it) 2. d = 1/2 a t 2 (from Galileo) 3. Inertial motion (his own corrected version) 4. F a 5. f of tension in a string 6. The relation between a planet s period and its distance from the sun

19 To find 5 - the tension in the cosmic string - Newton examined the case of a rock on a string

20 What factors affect the tension in the string?

21 f m v 2 /r

22 Now Newton applies this result to the moon case: f mv 2 /r v = d/t = 2πr/T f m(2πr/t) 2 /r = m(4π 2 r 2 /T 2 ) x 1/r m4π 2 r 2 T 2 x 1 r = m4π 2 r T 2

23 So f m4π 2 r T 2 But, from Kepler s Third Law T 2 r 3 m4π 2 r T 2 = Thus f m4π 2 r r 3 = 2 k r 2 m4π 2 r 2

24 f is 1 r 2 F At 1 earth radius: At 2 earth radii: 1 1 = some amount F r 2 1 F F 1 = (2) F 1

25 Newton s next move: To show that the moon (like apples) can be considered a falling body

26 From Newton s Principia Mathematica See for Animation yourself website

28 Two cases of projectile fall Thrown hard Thrown slowly

30 Since f a, a f f is also 1 r 2 Therefore a is 1 r 2 At 1 earth radius: At 2 earth radii: a= 32 ft/sec 2 a= 1/2 2 x 32 = 8 ft/sec 2

31 The moon is 60 earth radii away Therefore at the distance of the moon a = or x ft/sec 2

32 In one minute (60 sec) the moon will fall d = 1/2 a t 2 = 1/2 x x 60 2 = 16 feet

33 p = The same force that affects apples also affects the moon q = The moon falls 16 feet in one minute A. If p then q

34 p = The same force that affects apples also affects the moon q = The moon falls 16 feet in one minute A. If p then q B. Now he has to show q: the Moon actually does fall 16 ft in one minute

35 His task is to find BD, the distance the moon falls in a given amount of time. A B F D C. E

36 To find BD Newton thinks like an engineer A B F D C. E He is able to show that BD ~ 16 ft. AMAZING!!!!!

both d and e counted correct

both d and e counted correct 2. Which of the following did Aristotle not teach? a. Rest is a natural state and need not be explained further b. The speed of motion is directly proportional to the mover's force (v F) c. The speed of